Systems and methods for operating a quantum processor to determine energy eigenvalues of a Hamiltonian

ABSTRACT

Systems and methods for employing macroscopic resonant tunneling operations in quantum processors are described. New modes of use for quantum processor architectures employ probe qubits to determine energy eigenvalues of a problem Hamiltonian through macroscopic resonant tunneling operations. A dedicated probe qubit design that may be added to quantum processor architectures is also described. The dedicated probe qubit enables improved performance of macroscopic resonant tunneling operations and, consequently, improved performance of the new modes of use described.

BACKGROUND Field

The present systems and methods generally relate to quantum processors.

Adiabatic Quantum Computation

Adiabatic quantum computation typically involves evolving a system froma known initial Hamiltonian (the Hamiltonian being an operator whoseeigenvalues are the allowed energies of the system) to a finalHamiltonian by gradually changing the Hamiltonian. A simple example ofan adiabatic evolution is given by:H _(e)=(1−s)H _(i) +sH _(f)where H_(i) is the initial Hamiltonian, H_(f) is the final Hamiltonian,H_(e) is the evolution or instantaneous Hamiltonian, and s is anevolution coefficient which controls the rate of evolution. As thesystem evolves, the evolution coefficient s goes from 0 to 1 such thatat the beginning (i.e., s=0) the evolution Hamiltonian H_(e) is equal tothe initial Hamiltonian H_(i) and at the end (i.e., s=1) the evolutionHamiltonian H_(e) is equal to the final Hamiltonian H_(f). Before theevolution begins, the system is typically initialized in a ground stateof the initial Hamiltonian H_(i) and the goal is to evolve the system insuch a way that the system ends up in a ground state of the finalHamiltonian H_(f) at the end of the evolution. If the evolution is toofast, then the system can be excited to a higher energy state, such asthe first excited state. In the present systems and devices, an“adiabatic” evolution is considered to be an evolution that satisfiesthe adiabatic condition:{dot over (s)}|<1|dH _(e) /ds|0>|=δg ²(s)where {dot over (s)} is the time derivative of s, g(s) is the differencein energy between the ground state and first excited state of the system(also referred to herein as the “gap size”) as a function of s, and δ isa coefficient much less than 1. Generally the initial Hamiltonian H_(i)and the final Hamiltonian H_(f) do not commute; that is, [H₁, H_(f)]≠0.

The evolution process in adiabatic quantum computing may sometimes bereferred to as annealing. The rate that s changes, sometimes referred toas an evolution or annealing schedule, is normally slow enough that thesystem is always in the instantaneous ground state of the evolutionHamiltonian during the evolution, and transitions at anti-crossings(i.e., when the gap size is smallest) are avoided. Further details onadiabatic quantum computing systems, methods, and apparatus aredescribed in, for example, U.S. Pat. Nos. 7,135,701 and 7,418,283.

Quantum Annealing

Quantum annealing is a computation method that may be used to find alow-energy state, typically preferably the ground state, of a system.Somewhat similar in concept to classical annealing, the method relies onthe underlying principle that natural systems tend towards lower energystates because lower energy states are more stable. However, whileclassical annealing uses classical thermal fluctuations to guide asystem to its global energy minimum, quantum annealing may use quantumeffects, such as quantum tunneling, to reach a global energy minimummore accurately and/or more quickly than classical annealing. It isknown that the solution to a hard problem, such as a combinatorialoptimization problem, may be encoded in the ground state of a systemHamiltonian (e.g., the Hamiltonian of an (sing spin glass) and thereforequantum annealing may be used to find the solution to such a hardproblem. Adiabatic quantum computation may be considered a special caseof quantum annealing for which the system, ideally, begins and remainsin its ground state throughout an adiabatic evolution. Thus, those ofskill in the art will appreciate that quantum annealing systems andmethods may generally be implemented on an adiabatic quantum computer.Throughout this specification and the appended claims, any reference toquantum annealing is intended to encompass adiabatic quantum computationunless the context requires otherwise.

Quantum annealing uses quantum mechanics as a source of disorder duringthe annealing process. The optimization problem is encoded in aHamiltonian H_(P), and the algorithm introduces strong quantumfluctuations by adding a disordering Hamiltonian H_(D) that does notcommute with H_(P). An example case is:H _(E) ∝A(t)H _(D) +B(t)H _(P),where A(t) and B(t) are time dependent envelope functions. For example,A(t) changes from a large value to substantially zero during theevolution and H_(E) may be thought of as an evolution Hamiltoniansimilar to H_(e) described in the context of adiabatic quantumcomputation above. The disorder is slowly removed by removing H_(D)(i.e., reducing A(t)). Thus, quantum annealing is similar to adiabaticquantum computation in that the system starts with an initialHamiltonian and evolves through an evolution Hamiltonian to a final“problem” Hamiltonian H_(P) whose ground state encodes a solution to theproblem. If the evolution is slow enough, the system will typicallysettle in the global minimum (i.e., the exact solution), or in a localminimum close in energy to the exact solution. The performance of thecomputation may be assessed via the residual energy (difference fromexact solution using the objective function) versus evolution time. Thecomputation time is the time required to generate a residual energybelow some acceptable threshold value. In quantum annealing, H_(P) mayencode an optimization problem and therefore H_(P) may be diagonal inthe subspace of the qubits that encode the solution, but the system doesnot necessarily stay in the ground state at all times. The energylandscape of H_(P) may be crafted so that its global minimum is theanswer to the problem to be solved, and low-lying local minima are goodapproximations.

The gradual reduction of disordering Hamiltonian H_(D) (i.e., reducingA(t)) in quantum annealing may follow a defined schedule known as anannealing schedule. Unlike adiabatic quantum computation where thesystem begins and remains in its ground state throughout the evolution,in quantum annealing the system may not remain in its ground statethroughout the entire annealing schedule. As such, quantum annealing maybe implemented as a heuristic technique, where low-energy states withenergy near that of the ground state may provide approximate solutionsto the problem. The removal of the disordering Hamiltonian H_(D) mayoccur after the same Hamiltonian has been added. That, is turn thedisordering Hamiltonian H_(D) on and then off.

Persistent Current

A superconducting flux qubit may comprise a loop of superconductingmaterial (called a “qubit loop”) that is interrupted by at least oneJosephson junction. Since the qubit loop is superconducting, iteffectively has no electrical resistance. Thus, electrical currenttraveling in the qubit loop may experience no dissipation. If anelectrical current is coupled into the qubit loop by, for example, amagnetic flux signal, this current may continue to circulate around thequbit loop even when the signal source is removed. The current maypersist indefinitely until it is interfered with in some way or untilthe qubit loop is no longer superconducting (due to, for example,heating the qubit loop above its critical temperature). For the purposesof this specification, the term “persistent current” is used to describean electrical current circulating in the qubit loop of a superconductingqubit. The sign and magnitude of a persistent current may be influencedby a variety of factors, including but not limited to a flux signalΦ_(x) coupled directly into the qubit loop and a flux signal Φ_(CJJ)coupled into a compound Josephson junction that interrupts the qubitloop.

Quantum Processor

A quantum processor is any computer processor that is designed toleverage at least one quantum mechanical phenomenon (such assuperposition, entanglement, tunneling, etc.) in the processing ofquantum information. Many different designs for quantum processorhardware exist, including but not limited to: photonic quantumprocessors, superconducting quantum processors, nuclear magneticresonance quantum processors, ion-trap quantum processors, topologicalquantum processors, quantum dot quantum processors, etc. Regardless ofthe specific hardware implementation, all quantum processors encode andmanipulate quantum information in quantum mechanical objects or devicescalled quantum bits, or “qubits”; all quantum processors employstructures or devices for communicating information between qubits; andall quantum processors employ structures or devices for reading out astate of at least one qubit. The physical form of the qubits depends onthe hardware employed in the quantum processors; e.g., photonic quantumprocessors employ photon-based qubits, superconducting quantumprocessors employ superconducting qubits, and so on.

A quantum processor may be designed to operate in a variety of differentways. For example, a quantum processor may be designed as ageneral-purpose processor or as a special-purpose processor, and/or maybe designed to perform gate/circuit-based algorithms oradiabatic/annealing-based algorithms. Exemplary systems and methods forquantum processors are described in, for example: U.S. Pat. Nos.7,135,701, 7,418,283, 7,533,068, 7,619,437, 7,639,035, 7,898,282,8,008,942, 8,190,548, 8,195,596, 8,283,943, and US Patent ApplicationPublication 2011-0022820, each of which is incorporated herein byreference in its entirety.

The architecture of a quantum processor may be motivated by a desire toperform a specific type of task or algorithm. For example, a quantumprocessor may be designed specifically to perform Shor's Algorithm tofactor composite integers, or to perform quantum annealing to optimizean objective function, or to simulate a quantum system, etc. Thearchitecture of a quantum processor can therefore limit the diversity oftasks that can be performed by the quantum processor. There is a need inthe art to apply quantum processor architectures to implement new and/oralternative algorithms.

BRIEF SUMMARY

A method may be summarized as including programming a quantum processorincluding a plurality of superconducting flux qubits with a problemHamiltonian, the problem Hamiltonian has at least one energy eigenvalue;initializing a probe qubit from the plurality of superconducting fluxqubits; and scanning a transition rate of the probe qubit for a range ofenergy bias values of the probe qubit, the transition rate of the probequbit may at least partially depend on a difference between an energybias value of the probe qubit and an energy eigenvalue of the problemHamiltonian such that the at least one energy eigenvalue of the problemHamiltonian approximately corresponds to an energy bias value of theprobe qubit to produce a locally maximal transition rate of the probequbit. Programming the quantum processor may include initializing a setof computation qubits from the plurality of superconducting flux qubitsin the quantum processor with a respective energy bias for each qubit inthe set of computation qubits and a respective tunneling energy for eachqubit in the set of computation qubits; and initializing communicativecouplings between the computation qubits in the quantum processor with arespective coupling strength for each coupling device in the set ofcoupling devices. Initializing a probe qubit from the plurality ofsuperconducting flux qubits may include programming a tunneling energyof the probe qubit, the tunneling energy of the probe qubit may be lessthan the respective tunneling energies of the computation qubits; andcommunicatively coupling the probe qubit to at least one computationqubit. The probe qubit may be a superconducting flux qubit from theplurality of superconducting flux qubits that is not included in the setof computation qubits. Furthermore, the method may include programmingthe at least one computation qubit to which the probe qubit iscommunicatively coupled with a compensation signal to compensate for thecommunicative coupling between the probe qubit and the at least onecomputation qubit. Communicative coupling between the probe qubit andthe at least one computation qubit may be characterized by a couplingstrength J, the method may further include: adding a compensation signalto the at least one computation qubit to which the probe qubit iscommunicatively coupled, the compensation signal may have a magnitude ofat least approximately 2J and may be of opposite sign to the couplingstrength. Scanning a transition rate of the probe qubit for a range ofenergy bias values of the probe qubit may include, for a plurality ofenergy bias values for the probe qubit ranging from a first value to asecond value, iteratively: programming an energy bias of the probequbit; annealing the probe qubit; and measuring the transition rate ofthe probe qubit. Annealing the probe qubit may include lowering thetunneling energy of the probe qubit. The method may further include:initializing at least one additional probe qubit from the plurality ofsuperconducting flux qubits; and scanning a transition rate of the atleast one additional probe qubit for a range of energy bias values ofthe at least one additional probe qubit, the transition rate of the atleast one additional probe qubit may at least partially depend on adifference between an energy bias value of the at least one additionalprobe qubit and an energy eigenvalue of the problem Hamiltonian suchthat the at least one energy eigenvalue of the problem Hamiltonianapproximately corresponds to an energy bias value of the at least oneadditional probe qubit to produce a locally maximal transition rate ofthe at least one additional probe qubit. Initializing the at least oneadditional probe qubit may include: programming a tunneling energy ofthe at least one additional probe qubit, the tunneling energy of the atleast one additional probe qubit may be less than the respectivetunneling energies of the computation qubits; and communicativelycoupling the at least one additional probe qubit to at least onecomputation qubit. Scanning the transition rate of the at least oneadditional probe qubit may include, for a plurality of intermediateenergy bias values for the at least one additional probe qubit rangingfrom a first energy bias value to a second energy bias value,iteratively: programming an energy bias of the at least one additionalprobe qubit; annealing the at least one additional probe qubit; andmeasuring the transition rate of the at least one additional probequbit. Communicatively coupling the probe qubit to at least onecomputation qubit may include at least one of: galvanically coupling theprobe qubit to at least one computation qubit or inductively couplingthe probe qubit to at least one computation qubit. Communicativelycoupling the probe qubit to at least one computation qubit may includeprogramming a coupling device from the plurality of coupling devicesthat is not included in the set of computation coupling devices toprovide communicative coupling between the probe qubit and a computationqubit. The problem Hamiltonian may represent the Hamiltonian of aquantum system, and programming the quantum processor with the problemHamiltonian may include mapping the Hamiltonian of the quantum system tothe quantum processor. The Hamiltonian of a quantum system may include aHamiltonian of a molecular system, and mapping the Hamiltonian of thequantum system to the quantum processor by the programming subsystem mayinclude mapping the Hamiltonian of the molecular system to the quantumprocessor by the programming subsystem. Mapping the Hamiltonian of themolecular system to the quantum processor by the programming subsystemmay include using Jordan-Wigner transformations to map fermionicoperators of the molecular system to spin operators of the quantumprocessor by the programming subsystem. The transition rate of the probequbit may be at least partially dependent on a probability of the probequbit transitioning from a first state to a second state, and measuringthe transition rate of the probe qubit may include measuring a state ofthe probe qubit to determine whether or not a transition of the probequbit state has occurred. Initializing a probe qubit from the pluralityof superconducting flux qubits may include: programming a persistentcurrent of the probe qubit, the persistent current of the probe qubitmay be less than the respective persistent currents of the computationqubits; and communicatively coupling the probe qubit to at least onecomputation qubit. The probe qubit may be a superconducting flux qubitfrom the plurality of superconducting flux qubits that is not includedin the set of computation qubits. Programming a persistent current ofthe probe qubit may include programming a critical current of the probequbit.

A quantum processor may be summarized as including: a loop ofsuperconducting material having a geometric inductance L_(Gp); acompound Josephson junction that may interrupt the loop ofsuperconducting material, the compound Josephson junction may include atleast two Josephson junctions that are superconductingly electricallycoupled in parallel with one another with respect to the loop ofsuperconducting material; and a Josephson inductance L_(Jp) for the loopof superconducting material, wherein a magnitude of the Josephsoninductance L_(Jp) is greater than a magnitude of the geometricinductance L_(Gp). The quantum processor may further include: a number Nof Josephson junctions that interrupt the loop of superconductingmaterial, the N Josephson junctions being superconductingly electricallycoupled in series with the compound Josephson junction andsuperconductingly electrically coupled in series with one another withrespect to the loop of superconducting material, and wherein the NJosephson junctions positively contribute to the Josephson inductanceL_(Jp). N may be greater than or equal to 2. The quantum processor mayfurther include: a plurality of superconducting flux qubits, wherein theplurality of superconducting flux qubits define a Hamiltonian; aninductive coupling device to couple the loop of superconducting materialto at least one flux qubit from the plurality of superconducting fluxqubits with coupling strength J; and a local bias system for applying alocal bias with magnitude of about 2J and sign opposite to the couplingstrength, to the at least one flux qubit from the plurality ofsuperconducting flux qubits. The loop of superconducting material has apersistent current, the value of the persistent current may be less thanthe respective persistent currents of the at least one flux qubit fromthe plurality of superconducting flux qubits. The quantum processor mayfurther include a programming interface in a programming subsystem toapply a magnetic field to the compound Josephson junction thatinterrupts the loop of superconducting material, wherein varying themagnetic field may adjust the persistent current in the loop ofsuperconducting material.

A quantum processor may be summarized as including: a plurality ofcomputation qubits, where each computation qubit is a superconductingflux qubit that may include, respectively: a loop of superconductingmaterial having a length of at least X₁ and a geometric inductance of atleast L_(Gc); a compound Josephson junction that interrupts the loop ofsuperconducting material; and a Josephson inductance of at most L_(Jc),wherein a magnitude of the Josephson inductance L_(Jc) is less than amagnitude of the geometric inductance L_(Gc), at least one couplingdevice that provides tunable communicative coupling between a set of thecomputation qubits, wherein the at least one coupling device includes aloop of superconducting material interrupted by at least one Josephsonjunction; and a first probe qubit that may include: a loop ofsuperconducting material having a length less than X₁ and a geometricinductance L_(Gp); a compound Josephson junction that interrupts theloop of superconducting material of the first probe qubit, wherein thecompound Josephson junction includes at least two Josephson junctionsthat are superconductingly electrically coupled in parallel with oneanother with respect to the loop of superconducting material of thefirst probe qubit; and a Josephson inductance L_(Jp), wherein amagnitude of the Josephson inductance L_(Jp) is greater than a magnitudeof the geometric inductance L_(Gp), the first probe qubit may becommunicatively coupleable to at least one of the computation qubits.The quantum processor may further include: a second probe qubit that mayinclude: a loop of superconducting material having a length less than X₁and a geometric inductance of at most L_(Gp); a compound Josephsonjunction that interrupts the loop of superconducting material of thesecond probe qubit, wherein the compound Josephson junction includes atleast two Josephson junctions that are superconductingly electricallycoupled in parallel with one another with respect to the loop ofsuperconducting material of the second probe qubit; and a Josephsoninductance of at least L_(Jp), wherein a magnitude of the Josephsoninductance may be greater than a magnitude of the geometric inductance,the second probe qubit may be communicatively coupleable to at least oneof the computation qubits. The quantum processor may further include: aplurality of probe qubits, each probe qubit in the plurality of probequbits may include, respectively: a loop of superconducting materialhaving a length less than X₁ and a geometric inductance of at mostL_(Gp); a compound Josephson junction that interrupts the loop ofsuperconducting material, the compound Josephson junction including atleast two Josephson junctions that are superconductingly electricallycoupled in parallel with one another with respect to the loop ofsuperconducting material; and a Josephson inductance of at least L_(Jp),where a magnitude of the Josephson inductance is greater than amagnitude of the geometric inductance, each probe qubit in the pluralityof probe qubits is communicatively coupleable to at least one respectivecomputation qubit in the plurality of computation qubits. The firstprobe qubit may further include a number N of Josephson junctions thatinterrupt the loop of superconducting material of the first probe qubit,the N Josephson junctions being superconductingly electrically coupledin series with the compound Josephson junction of the first probe qubitand superconductingly electrically coupled in series with one anotherwith respect to the loop of superconducting material of the first probequbit, and wherein the N Josephson junctions positively contribute tothe Josephson inductance L_(Jp) of the first probe qubit. N may begreater than or equal to 2. Each computation qubit may further include,respectively, a total inductance L_(Tc) equal to a sum of the geometricinductance L_(Gc) and the Josephson inductance L_(Jc); the first probequbit may further include a total inductance L_(Tp) equal to a sum ofthe geometric inductance L_(Gp) and the Josephson inductance L_(Jp); andthe total inductance of the first probe qubit L_(Tp) may at leastapproximately equal to the total inductance of each computation qubitL_(Tc). The first probe qubit may be directly communicatively coupleableto at least one of the computation qubits via at least one of galvaniccoupling or inductive coupling. The quantum processor may furtherinclude: a coupling device that provides tunable communicative couplingbetween the first probe qubit and at least one of the computationqubits, the coupling device may include a loop of superconductingmaterial interrupted by at least one Josephson junction, and the firstprobe qubit may be communicatively coupleable to at least one of thecomputation qubits via the coupling device. The first probe qubit mayfurther include a first persistent current and each of the at least onecomputation qubits communicatively coupleable to the first probe qubitmay further include a second persistent current and the first persistentcurrent may be lower than the second persistent current.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

In the drawings, identical reference numbers identify similar elementsor acts. The sizes and relative positions of elements in the drawingsare not necessarily drawn to scale. For example, the shapes of variouselements and angles are not drawn to scale, and some of these elementsare arbitrarily enlarged and positioned to improve drawing legibility.Further, the particular shapes of the elements as drawn are not intendedto convey any information regarding the actual shape of the particularelements, and have been solely selected for ease of recognition in thedrawings.

FIG. 1 is a schematic diagram of a portion of an exemplarysuperconducting quantum processor designed for adiabatic quantumcomputation (and/or quantum annealing) that may be used and/or adaptedfor use in accordance with the present systems and methods.

FIG. 2A is a flow-diagram showing a method of operating a quantumprocessor to determine at least one energy eigenvalue of a Hamiltonianin accordance with the present systems and methods.

FIG. 2B is a flow-diagram showing a method of programming a quantumprocessor with a problem Hamiltonian by a programming subsystem, whichmay be executed in performing the method of operating a quantumprocessor of FIG. 2A in accordance with the present systems and methods.

FIG. 2C is a flow-diagram showing a method of initializing a probe qubitby a programming subsystem, which may be executed in performing themethod of operating a quantum processor of FIG. 2A in accordance withthe present systems and methods.

FIG. 2D is a flow-diagram showing a method of scanning a transition rateof a probe qubit for a range of energy bias values of the probe qubit,which may be executed in performing the method of operating a quantumprocessor of FIG. 2A in accordance with the present systems and methods.

FIG. 3 is a schematic diagram of a dedicated probe qubit in accordancewith the present systems and methods.

FIG. 4 is a schematic diagram of a quantum processor that includes adedicated probe qubit in accordance with the present systems andmethods.

FIG. 5 is a schematic diagram of another example implementation of aquantum processor that includes a dedicated probe qubit in accordancewith the present systems and methods.

DETAILED DESCRIPTION

In the following description, some specific details are included toprovide a thorough understanding of various disclosed embodiments. Oneskilled in the relevant art, however, will recognize that embodimentsmay be practiced without one or more of these specific details, or withother methods, components, materials, etc. In other instances,well-known structures associated with quantum processors, such asquantum devices, coupling devices, and control systems includingmicroprocessors, drive circuitry and nontransitory computer- orprocessor-readable media such as nonvolatile memory for instance readonly memory (ROM), electronically eraseable programmable ROM (EEPROM) orFLASH memory, etc., or volatile memory for instance static or dynamicrandom access memory (ROM) have not been shown or described in detail toavoid unnecessarily obscuring descriptions of the embodiments of thepresent systems and methods. Throughout this specification and theappended claims, the words “element” and “elements” are used toencompass, but are not limited to, all such structures, systems anddevices associated with quantum processors.

Unless the context requires otherwise, throughout the specification andclaims which follow, the word “comprise” and variations thereof, suchas, “comprises” and “comprising” are to be construed in an open,inclusive sense, that is as “including, but not limited to.”

Reference throughout this specification to “one embodiment,” or “anembodiment,” or “another embodiment” means that a particular referentfeature, structure, or characteristic described in connection with theembodiment is included in at least one embodiment. Thus, appearances ofthe phrases “in one embodiment,” or “in an embodiment,” or “anotherembodiment” in various places throughout this specification are notnecessarily all referring to the same embodiment. Furthermore, theparticular features, structures, or characteristics may be combined inany suitable manner in one or more embodiments.

It should be noted that, as used in this specification and the appendedclaims, the singular forms “a,” “an,” and “the” include plural referentsunless the content clearly dictates otherwise. Thus, for example,reference to a problem-solving system including “a quantum processor”includes a single quantum processor, or two or more quantum processors,including a grid or distributed network of multiple quantum processors.It should also be noted that the term “or” is generally employed in itssense including “and/or” unless the content clearly dictates otherwise.

The headings provided herein are for convenience only and do notinterpret the scope or meaning of the embodiments.

The various embodiments described herein provide systems and methods foroperating a quantum processor. More specifically, the variousembodiments described herein provide systems and methods for operating aquantum processor to perform new algorithms that determine energyeigenvalues of a problem Hamiltonian. The energy eigenvalues, andspecifically the energy differences between them, may collectively bereferred to as a spectrum. In some embodiments, the present systems andmethods may be used to find the spectrum of a Hamiltonian. TheHamiltonian may be a problem Hamiltonian that may be solved by thequantum processor. Furthermore, the present systems and methods may beused to determine entanglement in a plurality of qubits. The presentsystems and methods also describe new structures that may be added to aquantum processor architecture to facilitate implementation of thealgorithms described herein.

As an illustrative example, a superconducting quantum processor designedto perform adiabatic quantum computation and/or quantum annealing isused in the description that follows. However, as previously described,a person of skill in the art will appreciate that the present systemsand methods may be applied to any form of quantum processor hardware(e.g., superconducting, photonic, ion-trap, quantum dot, topological,etc.) implementing any form of quantum algorithm(s) (e.g., adiabaticquantum computation, quantum annealing, gate/circuit-based quantumcomputing, etc.).

An evolution Hamiltonian is proportional to the sum of a first termproportional to the problem Hamiltonian and a second term proportionalto the disordering Hamiltonian. As previously discussed, a typicalevolution may be represented by equation 1:H _(E) ∝A(t)H _(D) +B(t)H _(P)  (1)where H_(P) is the problem Hamiltonian, disordering Hamiltonian isH_(D), H_(E) is the evolution or instantaneous Hamiltonian, and A(t) andB(t) are an example of evolution coefficients which control the rate ofevolution. In general, evolution coefficients vary from 0 to 1. In someembodiments, a time varying evolution coefficient is placed on theproblem Hamiltonian. A common disordering Hamiltonian is shown inequation 2:

$\begin{matrix}{H_{D} \propto {{- \frac{1}{2}}{\sum\limits_{i = 1}^{N}{\Delta_{i}\sigma_{i}^{x}}}}} & (2)\end{matrix}$where N represents the number of qubits, σ_(i) ^(x) is the Paulix-matrix for the i^(th) qubit and Ai is the single qubit tunnelsplitting induced in the i^(th) qubit. Here, the σ_(i) ^(x) terms areexamples of “off-diagonal” terms. A common problem Hamiltonian includesfirst component proportional to diagonal single qubit terms and a secondcomponent proportional to diagonal multi-qubit terms. The problemHamiltonian, for example, may be of the form:

$\begin{matrix}{H_{P} \propto {- {\frac{ɛ}{2}\lbrack {{\sum\limits_{i = 1}^{N}{h_{i}\sigma_{i}^{z}}} + {\sum\limits_{j > i}^{N}{J_{ij}\sigma_{i}^{z}\sigma_{j}^{z}}}} \rbrack}}} & (3)\end{matrix}$where N represents the number of qubits, σ_(i) ^(z) is the Pauliz-matrix for the i^(th) qubit, h_(i) and J_(i,j) are dimensionless localfields coupled into each qubit, and ε is some characteristic energyscale for H_(p). Here, the σ_(i) ^(z) and σ_(i) ^(z)σ_(j) ^(z) terms areexamples of “diagonal” terms. The former is a single qubit term and thelatter a two qubit term. Throughout this specification, the terms “finalHamiltonian” and “problem Hamiltonian” are used interchangeably.Hamiltonians such as H_(D) and H_(P) in equations 2 and 3, respectively,may be physically realized in a variety of different ways. A particularexample is realized by an implementation of superconducting qubits.

FIG. 1 is a schematic diagram of a portion of an exemplarysuperconducting quantum processor 100 designed for AQC (and/or quantumannealing) that may be used and/or adapted for use in accordance withthe present systems and methods. The portion of superconducting quantumprocessor 100 shown in FIG. 1 includes two superconducting qubits 101,102 and a tunable ZZ-coupler 111 coupling information therebetween(i.e., providing pair-wise coupling between qubits 101 and 102). Whilethe portion of quantum processor 100 shown in FIG. 1 includes only twoqubits 101, 102 and one coupler 111, those of skill in the art willappreciate that quantum processor 100 may include any number of qubitsand any number of coupling devices coupling information therebetween.

The portion of quantum processor 100 shown in FIG. 1 may be implementedto physically realize AQC and/or QA by initializing the system with theHamiltonian described by equation 2 and evolving the system to theHamiltonian described by equation 3 in accordance with the evolutiondescribed by equation 1. Quantum processor 100 includes a plurality ofinterfaces 121-125 that are used to configure and control the state ofquantum processor 100. Each of interfaces 121-125 may be realized by arespective inductive coupling structure, as illustrated, as part of aprogramming subsystem. Such a programming subsystem may be separate fromquantum processor 100, or it may be included locally (i.e., on-chip withquantum processor 100) as described in, for example, U.S. Pat. Nos.7,876,248 and 8,035,540.

In the operation of quantum processor 100, interfaces 121 and 124 mayeach be used to couple a flux signal into a respective compoundJosephson junction 131,132 of qubits 101 and 102, thereby realizing theA terms in the system Hamiltonian. This coupling provides theoff-diagonal of terms of the Hamiltonian described by equation 2 andthese flux signals are examples of “tunneling energies” and/or“disordering signals.” Similarly, interfaces 122 and 123 may each beused to couple a flux signal (i.e., an energy bias) into a respectivequbit loop of qubits 101 and 102, thereby realizing the h_(i) terms inthe system Hamiltonian. This coupling provides the diagonal σ^(z) termsof equation 3. Furthermore, interface 125 may be used to couple a fluxsignal into coupler 111, thereby realizing the J_(ij) term(s) in thesystem Hamiltonian which control the coupling strength(s) of thecoupler(s). This coupling provides the diagonal σ^(z) _(i)σ^(z) _(j)terms of equation 3. In FIG. 1, the contribution of each of interfaces121-125 to the system Hamiltonian is indicated in boxes 121 a-125 a,respectively. Thus, throughout this specification and the appendedclaims, the terms “problem formulation” and “configuration of a numberof programmable parameters” are used to refer to, for example, aspecific assignment of h_(i) and J_(ij) terms in the system Hamiltonianof a superconducting quantum processor via, for example, interfaces121-125.

In the context of quantum processor 100, the term “programmingsubsystem” is used to generally describe the interfaces (e.g.,“programming interfaces” 121-125) used to apply and/or evolve theprogrammable parameters (e.g., the Δ_(i), h_(i) and J_(ij) terms) to theprogrammable elements of quantum processor 100 and other associatedcontrol circuitry and/or instructions. As previously described, theprogramming interfaces of the programming subsystem may communicate withother subsystems which may be separate from the quantum processor or maybe included locally on the processor.

Quantum processor 100 also includes readout devices 141 and 142, wherereadout device 141 is configured to read out the state of qubit 101 andreadout device 142 is configured to read out the state of qubit 102. Inthe embodiment shown in FIG. 1, each of readout devices 141 and 142comprises a respective DC-SQUID that is configured and positioned toinductively couple to the corresponding qubit (qubits 101 and 102,respectively). In the context of quantum processor 100, the term“readout subsystem” is used to generally describe the readout devices141, 142 used to read out the final states of the qubits (e.g., qubits101 and 102) in the quantum processor to produce a bit string. Thereadout subsystem may also include other elements, such as routingcircuitry (e.g., latching elements, a shift register, or a multiplexercircuit) and/or may be arranged in alternative configurations (e.g., anXY-addressable array, an XYZ-addressable array, etc.). Qubit readout mayalso be performed using alternative circuits, such as that described inPCT Patent Application Publication 2012-064974.

While FIG. 1 illustrates only two physical qubits 101, 102, one coupler111, and two readout devices 141, 142, a quantum processor (e.g.,processor 100) may employ any number of qubits, couplers, and/or readoutdevices, including a larger number (e.g., hundreds, thousands or more)of qubits, couplers and/or readout devices. The application of theteachings herein to processors with a different (e.g., larger) number ofcomputational components should be readily apparent to those of ordinaryskill in the art.

At least some of the devices illustrated in FIG. 1 are simplified inorder to enhance clarity. As an example, the structure of the qubits(101, 102) and the interface to the readout devices (141, 142) aresimplified in FIG. 1 in order to reduce clutter. While the simplifiedcircuits of quantum processor 100 may be sufficient for someapplications, a quantum processor may employ qubit circuits and/orreadout schemes that are considerably more complicated than those whichare illustrated in FIG. 1.

The elements of a quantum processor (e.g., a superconducting quantumprocessor designed to perform adiabatic quantum computation and/orquantum annealing such as processor 100 from FIG. 1) may be used toperform and/or manipulate macroscopic resonant tunneling as describedin, at least: M. H. S. Amin et al., “Macroscopic Resonant Tunneling inthe Presence of Low Frequency Noise”, Phys. Rev. Lett. 100, 197001(2008); R. Harris et al., “Probing Noise in Flux Qubits via MacroscopicResonant Tunneling”, Phys. Rev. Lett. 101, 117003 (2008); T. Lanting etal., “Cotunneling in pairs of coupled flux qubits,” Phys. Rev. B 82,060512(R) (2010); and T. Lanting et al., “Probing high-frequency noisewith macroscopic resonant tunneling,” Phys. Rev. B 83, 180502 (2011), A.J. Berkley et al., “Tunneling spectroscopy using a probe qubit” Phys.Rev. B 87, 020502(R) (2013); hereafter “Berkley”, each of which isincorporated herein by reference in its entirety. In accordance with thepresent systems and methods, the techniques for macroscopic resonanttunneling described in the above-listed publications may be employed incomputational algorithms, such as for example in algorithms foroperating a quantum processor to determine energy eigenvalues of aHamiltonian. Furthermore, in some embodiments, the present systems andmethods also describe new structures that may be added to a quantumprocessor to facilitate macroscopic resonant tunneling operations and/orto facilitate operating the quantum processor to determine energyeigenvalues of a Hamiltonian.

The computational algorithms described herein generally involve using afirst qubit in a quantum processor to probe a characteristic orcharacteristics of at least one other qubit in the quantum processor. Inthis configuration, the first qubit that performs the probing isreferred to as a “probe qubit” and the at least one other qubit isreferred to as a “computation qubit.” The computation qubit(s) mayencode a problem Hamiltonian and the probe qubit may probe acharacteristic or characteristics of the problem Hamiltonian by using,for example, a macroscopic resonant tunneling process to probe acharacteristic or characteristics of the computation qubit(s). Thus,throughout this specification and the appended claims, the term “problemHamiltonian” is used to refer to a Hamiltonian that is programmed intothe qubits of a quantum processor (e.g., of the form shown in equation3), the term “computation qubit” is used to refer to a qubit that isprogrammed to represent, map, or encode at least a portion of theproblem Hamiltonian when the problem Hamiltonian is programmed into thequbits of the quantum processor, and the term “probe qubit” is used torefer to a qubit that is used to measure, scan, monitor, or otherwiseprobe at least one characteristic of the problem Hamiltonian bymeasuring, scanning, monitoring, or otherwise probing at least onecharacteristic of at least one of the computation qubits in the quantumprocessor. For example, in some embodiments, a probe qubit may be usedto determine the entanglement in a plurality of computational qubits.

FIG. 2A is a flow-diagram showing a method 200 a of operating a quantumprocessor to determine at least one energy eigenvalue of a Hamiltonianin accordance with the present systems and methods. Method 200 aincludes three acts 201, 202, and 203, though those of skill in the artwill appreciate that in alternative embodiments certain acts may beomitted and/or additional acts may be added. Those of skill in the artwill appreciate that the illustrated order of the acts is shown forexemplary purposes only and may change in alternative embodiments. Eachof acts 201-203 may, in some embodiments, include multiple sub-acts asdescribed in more detail in FIGS. 2B, 2C, and 2D.

At 201, the quantum processor is programmed with a problem Hamiltonianby a programming subsystem. The problem Hamiltonian may include at leastone energy eigenvalue. The quantum processor may be similar to quantumprocessor 100 from FIG. 1 though may include any number of qubits. Forexample, the quantum processor may comprise a plurality ofsuperconducting flux qubits (e.g., 101, 102) and the programmingsubsystem may include a plurality of programming interfaces (e.g.,121-125). Thus, programming the quantum processor with a problemHamiltonian may include programming at least a subset of thesuperconducting flux qubits in the quantum processor as computationqubits.

At 202, a probe qubit is initialized by the programming subsystem. Theprobe qubit may be a superconducting flux qubit in the quantum processorthat is not used as a computation qubit. For example, the probe qubitmay be a superconducting flux qubit in the quantum processor that is notprogrammed to represent, map, or encode at least a portion of a problemHamiltonian at 201. Initializing the probe qubit may involvecommunicatively coupling the probe qubit with at least one computationqubit in the quantum processor. The probe qubit may not need to beweakly coupled to at least one computation qubit in the quantumprocessor. For example, a probe qubit may be coupled with a computationqubit characterized by a coupling strength J, with a magnitude of a biasof approximately 2J applied to the computation qubit. In someembodiments, the value of the coupling strength J may be negative or anantiferromagnetic coupling.

At 203, a transition rate of the probe qubit is scanned for a range ofenergy bias values of the probe qubit in order to perform “tunnelingspectroscopy” of the computation qubit(s). The “transition rate” of theprobe qubit may refer to, for example, transitions between the energystates of the probe qubit by a macroscopic resonant tunneling process.For example, the potential energy of the probe qubit may be representedby a double-well potential and the energy state of the probe qubit maybe an energy state within one of the two wells. Macroscopic resonanttunneling transitions refer to transitions in the energy state of theprobe qubit from a first well to a second well in the double-wellpotential by quantum tunneling through the energy barrier that separatesthe two wells. The energy bias value may correspond to an amount of“tilt” controlling the relative depths of the two wells in thedouble-well potential. An energy state of the probe qubit may, forexample, be deliberately programmed to correspond to a first well of thedouble-well potential that is of higher energy than a second well of thedouble-well potential so that a macroscopic resonant tunneling operationmay be used to transition the energy state of the probe qubit from thefirst well to the second well. Thus, the “transition rate” may be atleast partially dependent on a probability of the probe qubittransitioning from a first state to a second state via a macroscopicresonant tunneling process. The transition rate of the probe qubit mayat least partially depend on a difference between an energy bias valueof the probe qubit and an energy eigenvalue of the problem Hamiltoniansuch that at least one energy eigenvalue of the problem Hamiltonian atleast approximately corresponds to an energy bias value of the probequbit that produces a locally maximal transition rate of the probequbit. In other words, scanning a transition rate of the probe qubit fora range of energy bias values of the probe qubit may involve measuring atransition rate of the probe qubit for multiple energy bias values ofthe probe qubit in order to determine an energy bias value of the probequbit that produces a local maximum, peak, or spike in the transitionrate of the probe qubit.

As previously described, each of acts 201-203 from method 200 a may, insome embodiments, include multiple acts or sub-acts. Exemplaryacts/sub-acts are now described in FIGS. 2B, 2C, and 2D

FIG. 2B is a flow-diagram showing a method 200 b of programming aquantum processor with a problem Hamiltonian by a programming subsystem,which may be executed in performing act 201 from method 200 a of FIG. 2Ain accordance with the present systems and methods. Method 200 bincludes five acts or sub-acts 211, 211 a, 211 b, 212, and 212 a, thoughthose of skill in the art will appreciate that in alternativeembodiments certain acts/sub-acts may be omitted and/or additionalacts/sub-acts may be added. Those of skill in the art will appreciatethat the illustrated order of the acts/sub-acts is shown for exemplarypurposes only and may change in alternative embodiments.

At 211, a set of computation qubits in the quantum processor isinitialized by the programming subsystem. Initializing the set ofcomputation qubits may include programming a respective energy bias ofeach qubit in the set of computation qubits by the programming subsystemat 211 a (e.g., programming the respective h_(i) term of eachcomputation qubit as described for FIG. 1) and/or programming arespective tunneling energy of each qubit in the set of computationqubits by the programming subsystem at 211 b (e.g., programming therespective Δ_(i) term of each computation qubit as described in FIG. 1).The set of computation qubits must include at least one computationqubit but may include any number of computation qubits that is greaterthan or equal to one (e.g., tens, hundreds, thousands, or millions ofcomputation qubits, etc.).

The quantum processor may include a plurality of coupling devices thatprovide tunable communicative coupling between respective sets of thecomputation qubits. At 212, a set of computation coupling devices in thequantum processor is initialized by the programming subsystem.Throughout this specification and the appended claims, the term“computation coupling device” is used to refer to a coupling device thatis programmed to represent, map, or encode at least a portion of aproblem Hamiltonian when a quantum processor is programmed with aproblem Hamiltonian. Initializing the set of computation couplingdevices may include programming a respective coupling strength of eachcoupling device in the set of computation coupling devices by theprogramming subsystem at 212 a (e.g., programming the respective term ofeach computation coupling device as described in FIG. 1). The set ofcomputation coupling devices must include at least one computationcoupling device but may include any number of computation couplingdevices that is greater than or equal to one.

FIG. 2C is a flow-diagram showing a method 200 c of initializing a probequbit by a programming subsystem, which may be executed in performingact 202 from method 200 a of FIG. 2A in accordance with the presentsystems and methods. Method 200 c includes two acts 221 and 222, thoughthose of skill in the art will appreciate that in alternativeembodiments certain acts may be omitted and/or additional acts may beadded. Those of skill in the art will appreciate that the illustratedorder of the acts is shown for exemplary purposes only and may change inalternative embodiments.

At 221, a tunneling energy of the probe qubit is programmed by theprogramming subsystem. Programming a tunneling energy of the probe qubitmay include applying a flux bias to the probe qubit (i.e., to a compoundJosephson junction of the probe qubit) via a programming interface torealize a first A term in the probe qubit. The tunneling energy of theprobe qubit may be significantly less than the respective tunnelingenergies of the computation qubits, which may enable the computationqubits to be operated in a higher frequency regime than the probe qubit.This configuration is advantageous in quantum processor architecturesthat have limited signal bandwidth, since the probe qubit may beoperated within the range of the limited signal bandwidth while thecomputation qubits may be operated outside of this limited range (i.e.,at higher frequency ranges). Therefore, it may allow for ease ofbuilding greater scaling of the quantum processor without the need toscale the number of control lines.

At 222, the probe qubit is communicatively coupled to at least onecomputation qubit. The probe qubit may be directly communicativelycoupled to at least one computation qubit (e.g., via direct inductive orgalvanic coupling), or the probe qubit may be indirectly communicativelycoupled to at least one computation qubit (e.g., via a coupling device).

FIG. 2D is a flow-diagram showing a method 200 d of scanning atransition rate of the probe qubit for a range of energy bias values ofthe probe qubit, which may be executed in performing act 203 from method200 a of FIG. 2A in accordance with the present systems and methods.Method 200 d includes five acts 231, 232, 233, 234 and 235, though thoseof skill in the art will appreciate that in alternative embodimentscertain acts may be omitted and/or additional acts may be added. Thoseof skill in the art will appreciate that the illustrated order of theacts is shown for exemplary purposes only and may change in alternativeembodiments.

At 231, an iteration cycle is initiated. Since act 203 from method 200 ainvolves scanning a transition rate of the probe qubit for a range ofenergy bias values of the probe qubit, the scanning may be doneiteratively using a different energy bias of the probe qubit in eachiteration. The iteration cycle may include acts 232, 233, and 234.

At 232, the energy bias of the probe qubit is programmed by theprogramming subsystem. Programming an energy bias of the probe qubit mayinclude applying a flux bias to the probe qubit via a programminginterface to realize a diagonal single qubit term (e.g. h_(i) term) inthe probe qubit. The energy bias may correspond to a “tilt” (i.e., adifference in the relative depths of the two wells) in the double-wellpotential of the probe qubit.

At 233, the probe qubit is annealed by the programming subsystem.Annealing the probe qubit may include varying the tunneling energy ofthe probe qubit via a programming interface to increase the height ofthe energy barrier that separates the two wells in the double-wellpotential of the probe qubit, thereby causing a state of the probe qubitto localize in one of the two wells.

At 234, the transition rate of the probe qubit is measured by a readoutsubsystem. The transition rate of the probe qubit may refer totransitions between the energy states of the probe qubit that resultfrom resonant tunneling through the energy barrier that separates thetwo wells in the double-well potential of the probe qubit, where thetransition rate of the probe qubit is locally maximal (i.e., exhibits alocal maximum, peak, or spike) when an energy bias value of the probequbit causes an energy state of the probe qubit to resonate with (e.g.,substantially equate or align with) an energy eigenvalue of the problemHamiltonian embodied by the computation qubit(s) to which the probequbit is communicatively coupled.

At 235, the iteration cycle is terminated. Thus, acts 232, 233, and 234are iterated for multiple different energy bias values of the probequbit and the iteration cycle is terminated at 235 when, for example: adesired number or range of energy bias values has been used, at leastone energy eigenvalue of the problem Hamiltonian has been identified,and/or a maximum desired amount of computation time has elapsed.

Certain acts of method 200 a of FIG. 2A (and consequently certainacts/sub-acts of method 200 b of FIG. 2B, method 200 c of FIG. 2C,and/or method 200 d of FIG. 2D) make reference to a probe qubit. Inaccordance with the present systems and methods, any or all of the actsand/or sub-acts of FIGS. 2A, 2B, 2C, and/or 2D may be completed bymultiple probe qubits within a single quantum processor. For example,methods 200 a, 200 b, 200 c, and 200 d (including all associated actsand sub-acts thereof) may be carried out using only one probe qubit, ormultiple times either in series or in parallel using multiple probequbits. Thus, in some embodiments, methods 200 a, 200 b, 200 c, and 200d (including all associated acts and sub-acts thereof) may be completedusing a first probe qubit and at least one additional probe qubit, suchas a second probe qubit.

The present systems and methods describe new modes of use for quantumprocessor hardware. For example, quantum processor 100 from FIG. 1 isused in the art to find a low-energy configuration (such as the groundstate energy configuration) of a problem Hamiltonian, where the problemHamiltonian specifies a set of constraints. The energy configuration isreturned as a bit-string representing a configuration of qubit statesthat satisfactorily complies with the constraints imposed by the problemHamiltonian. The modes of use described herein involve determiningenergy eigenvalues of a Hamiltonian without the need to measure theconfiguration of the qubit states. Such contrasts from returning abit-string as a solution, where the bit-string represents aconfiguration of qubit states that corresponds to a low-energyconfiguration under the conditions specified by the problem Hamiltonian.The energy eigenvalues of a Hamiltonian (e.g., a problem Hamiltonianthat is embodied by a system of any number of computation qubits) arediscrete-valued characteristics of the Hamiltonian that, in the presentsystems and methods, are probed via at least one probe qubit. Thus, themodes of use described herein involve returning discrete values assolutions, where the discrete values correspond to characteristics of asystem of interacting computation qubits that embody a problemHamiltonian. In contrast to determining a configuration that produces alow-energy state of a problem Hamiltonian, the modes of use describedherein involve determining the value of at least one low-energy state ofthe problem Hamiltonian (e.g., the value of the ground state energy ofthe problem Hamiltonian) and/or the values of multiple low-energy statesof the problem Hamiltonian.

A person of skill in the art will appreciate that determining energyeigenvalues of a Hamiltonian (e.g., energy eigenvalues of a problemHamiltonian) may be of significant utility and/or value in manydifferent scenarios. As an example, the problem Hamiltonian mayrepresent the Hamiltonian of a molecular system (e.g., the Hamiltonianof a specific molecule, such as a drug molecule) and determining theenergy eigenvalues of the molecular system may provide critical insightinto the behavior, composition, or function of the molecular system. Inaccordance with the present systems and methods, the Hamiltonian of amolecular system may be mapped onto a set of computation qubits in asuperconducting quantum processor such as processor 100 from FIG. 1 byusing Jordan-Wigner transformations to map fermionic operators of themolecular system to spin operators of the quantum processor. Techniquesfor employing Jordan-Wigner transformations would be understood by aperson of skill in the art and are described in, for example, Michael A.Nielsen, “The Fermionic canonical commutation relations and theJordan-Wigner transform,” dated Jul. 29, 2005, available online,accessed May 30, 2013.

In methods 200 a, 200 b, 200 c, and 200 d, a set of computation qubitsmay be programed to represent a problem Hamiltonian and at least oneprobe qubit may be communicatively coupled to at least one of thecomputation qubits. In this configuration, the at least one probe qubitmay not be programmed to represent a portion of the problem Hamiltonian;however, communicative coupling between the probe qubit and acomputation qubit may perturb the programming signals (e.g., energybiases) that are applied to the computation qubit. Such perturbation mayalso perturb the problem Hamiltonian. In accordance with the presentsystems and methods, such perturbations may be compensated by applying acompensation signal to at least the computation qubit that iscommunicatively coupled to the probe qubit. For example, method 200 amay include the additional act or sub-act of programming the at leastone computation qubit to which the probe qubit is communicativelycoupled with a compensation signal by the programming subsystem tocompensate for the communicative coupling between the probe qubit andthe at least one computation qubit. Communicative coupling between theprobe qubit and the at least one computation qubit may be characterizedby a coupling strength J. In some embodiments, programming the at leastone computation qubit to which the probe qubit is communicativelycoupled includes adding a compensation signal by the programmingsubsystem providing a local bias of a magnitude of at leastapproximately 2J. In some embodiments, the added compensation signalprovides a local bias of approximately 2J. In some embodiments, theadded compensation signal may be of opposite sign to the couplingstrength. As described in more detail in Berkley, this compensationscheme can improve the resolution of the energy eigenvalues of theproblem Hamiltonian and facilitate resonant tunneling operations betweenthe probe qubit and the computation qubit(s).

In some embodiments, the probe qubit may have a large energy barrier anda corresponding low probability of quantum tunneling. In someembodiments, the probe qubit may be similar to a computation qubit,where the computation qubit may have a lower energy barrier with ahigher probability of quantum tunneling. The coupling of the probe qubitto the at least one computation qubit supports a method to determine thespectrum of the at least one computation qubit. By adjusting the probequbit bias and looking for changes in escape rate from the energeticisolated state to another leads to information on the state of the probequbit coupled to the at least one computation qubit. This process isconceptually similar to macroscopic resonant tunneling. Local peaks inthe escape rate imply an alignment of energy levels on either side of abarrier to effect macroscopic resonant tunneling through a barrier. Thealignment occurs by changing the bias on the system. The differences inthe locations in units of bias of the local peaks of the escape rate canbe converted to differences in the energy levels of the Hamiltonian.

As previously described, the present systems and methods provide newmodes of use for quantum processors. In addition, in some embodiments,the present systems and methods provide new structures that may be addedto quantum processors in order to, for example, facilitate and/orimprove the performance of macroscopic resonant tunneling operationsand/or the performance of the new modes of use described herein. Inaccordance with the present systems and methods, a quantum processor mayinclude at least one dedicated probe qubit that is structurally designedto perform the functions of a probe qubit as described herein andstructurally distinct from a computation qubit.

Tunneling spectroscopy of a large system of communicatively coupledcomputation qubits may be used for qubit entanglement studies and todemonstrate quantum simulation. However, as the at least one probe qubitcommunicatively coupled to the system of communicatively coupledcomputation qubits is annealed, the spectroscopic energy resolution(i.e., spectral resolution) may be limited by incoherent broadening inthe probe qubit. In other words, when each eigenstate of the probe qubitis fit to a Gaussian distribution with the peaks of the distributioncorresponding to the energy bias values of the probe qubitcommunicatively coupled to the computation qubit system that producelocally maximal transition rates of the probe qubit, the width of eachpeak of the Gaussian distribution (for example, full width half maximum)may be too broad making it difficult to distinguish between the specificeigenstates of the probe qubit. This may reduce/hinder spectroscopiccapabilities of the probe qubit. The energy broadening, for qubittunneling spectroscopy with a probe device may be given as arelationship proportional to the product of the width of the broadeningobserved and the persistent current of the probe qubit. An example ofthis:R=2W _(phi) I _(p)  (4)where W_(phi) is the width (in observed units such as flux unit) of thebroadening and I_(p) is the persistent current of the probe qubit. Theobjective is to reduce R such that narrower peaks within the Gaussiandistribution may be obtained. R may be reduced by reducing W_(phi)and/or I_(p). For example, increasing the Josephson inductance of theprobe qubit may reduce noise and therefore reduce W_(phi). Reducing thecritical current I_(c) of the probe qubit by a similar factor may reduceI_(p).

Reducing these factors, (e.g., persistent current of the probe qubit,width of the broadening in flux units by increasing the Josephsoninductance of the probe qubit, width of the broadening in energy units)leads to narrower peaks and improved spectral resolution.

FIG. 3 is a schematic diagram of a dedicated probe qubit 300 inaccordance with the present systems and methods. Probe qubit 300 issimilar to superconducting flux quits 101 and 102 from FIG. 1 in that itcomprises a loop of superconducting material 301 interrupted by acompound Josephson junction 302. Compound Josephson junction 302includes at least two Josephson junctions 321, 322 that aresuperconductingly electrically coupled in parallel with one another withrespect to loop of superconducting material 301. However, probe qubit300 further comprises additional Josephson junctions (e.g., ten shown)330-339 that interrupt loop of superconducting material 301 and aresuperconductingly electrically coupled in series with one another andsuperconductingly electrically coupled in series with compound Josephsonjunction 302 with respect to loop of superconducting material 301. Inaccordance with the present systems and methods, these additionalJosephson junctions 330-339 are included in probe qubit 300 in order topositively contribute to the Josephson inductance L_(Jp) of probe qubit300.

A superconducting flux qubit, such as either of qubits 101 and 102 fromFIG. 1, typically exhibits a total inductance L_(T) that is at leastpartially given by the sum of a geometric inductance L_(G) and aJosephson inductance L_(J) (i.e., L_(T)≈L_(G)+L_(J)). The geometricinductance L_(G) is a characteristic that arises due, at least in part,to the inductance of the wiring that forms the qubit. For example, thegeometric inductance L_(G) of qubit 101 from FIG. 1 results, at least inpart, from the inductance of the wiring that forms the loop ofsuperconducting material and the compound Josephson junction 131. Themagnitude of the geometric inductance L_(G) depends on, among otherthings, the length, width, and geometry of the wiring of the qubit. Onthe other hand, the Josephson inductance L_(J) is a characteristic thatarises, at least in part, due to the inductance of the Josephsonjunction(s) that interrupt the wiring of the qubit. For example, theJosephson inductance L_(J) of qubit 101 from FIG. 1 results, at least inpart, from the inductance of the Josephson junctions in compoundJosephson junction 131. The magnitude of the Josephson inductance L_(J)depends on, among other things, the size and number of Josephsonjunctions in the qubit.

In quantum processors that employ communicatively coupleablesuperconducting flux qubits (e.g., processor 100 from FIG. 1), thewiring of each superconducting flux qubit is typically quite longbecause the qubit body must provide sufficient space and inductance topermit communicative couplings to multiple other qubits. As a result,superconducting flux qubits that are designed to be operated ascomputation qubits (i.e., superconducting flux qubits that arecommunicatively coupleable to multiple other superconducting flux qubitsand are to be used to encode at least a portion of a problemHamiltonian) typically have a large geometric inductance L_(G) comparedto their Josephson inductance L_(J). In other words, for a computationqubit (denoted by subscript “c” in the symbols that follow),L_(Gc)>L_(Jc), sometimes by several orders of magnitude.

In accordance with the present systems and methods, the performance of aprobe qubit may be advantageously enhanced if: a) the persistent currentI_(p) is reduced, b) the geometric inductance L_(G) is reduced, and c)this reduction in the geometric inductance is at least partially offsetand/or compensated for by an increase in the Josephson inductance L_(J).In other words, for a probe qubit (denoted by subscript “p” in thesymbols that follow), it can be advantageous if L_(Jp)>L_(Gp), sometimesby several orders of magnitude. Probe qubit 300 from FIG. 3 provides anexemplary design for how the geometric inductance L_(Gp) can be reducedand how the Josephson inductance L_(Jp) can be made to exceed thegeometric inductance L_(Gp). Namely, probe qubit 300 comprises a loop ofsuperconducting material 301 that is comparatively shorter than the loopof superconducting material of a typical computation qubit (e.g.,shorter than the loop of superconducting material in either ofsuperconducting flux qubits 101 and/or 102 from FIG. 1) in order toreduce the geometric inductance L_(Gp) of probe qubit 300 and probequbit 300 includes several Josephson junctions (i.e., ten Josephsonjunctions 330-339) superconducting electrically coupled in series withone another in loop of superconducting material 301 in order topositively contribute to (i.e., enhance) the Josephson inductance L_(Jp)of probe qubit 300. Those of skill in the art will appreciate that thenumber of Josephson junctions shown in probe qubit 300 (i.e., tenJosephson junctions 330-339) is used for exemplary purposes only and, inpractice, a dedicated probe qubit may employ any number of Josephsonjunctions that provide sufficient L_(Jp)>L_(Gp). Furthermore, thepersistent current of a probe qubit may be reduced (i.e., lower than thepersistent current of a computation qubit) by reducing the criticalcurrent of the probe qubit. In FIG. 3, programming interface 342 may beused to adjust the critical current of probe qubit 300. For example, thecritical current of a probe qubit may be reduced to approximately halfthe critical current of a computation qubit such that the persistentcurrent of the probe qubit may be approximately half of that of thecomputation qubit at a given tunneling energy.

At least one advantage of a probe qubit design that embodiesL_(Jp)>L_(Gp) and a lower I_(p) than that of a computation qubit is thatsuch a device may provide significantly better spectral resolution(e.g., produce significantly narrower peaks during magnetic resonanttunneling) than a typical computation qubit for which L_(Gp)>L_(Jp) anda corresponding higher I_(p). During the fabrication of anysuperconducting qubit, defects may develop in the wiring and/ordielectric layers and these defects may act as sources of noise thatadversely affect the performance of the qubit. In the design of adedicated probe qubit (e.g., probe qubit 300 from FIG. 3), the wiringlength is truncated (i.e., L_(Gp) is reduced) in order to reducecoupling between the defects and the qubit itself and thereby reduce theeffect these defects have on the performance of the qubit. For example,if a computation qubit has a loop of superconducting material of lengthX₁, then the probe qubit advantageously has a loop of superconductingmaterial of length <X₁. However, this reduction in the geometricinductance L_(Gp) has a reductive effect on the total inductance of theprobe qubit L_(Tp). In order to compensate for this reductive effect andprovide a total inductance L_(Tp) in the correct parametric range formacroscopic resonant tunneling operations, a number of additionalJosephson junctions are added to the qubit body (e.g., Josephsonjunctions 330-339 from FIG. 3) to augment the Josephson inductanceL_(Jp) of the probe qubit. Thus, the design of probe qubit 300 (namely,realizing L_(Jp)>L_(Gp)) provides significantly reduced coupling todefect noise (via reduced wiring length and L_(Gp)) while usingaugmented Josephson inductance L_(Jp) to maintain a total inductanceL_(Tp) that is sufficient for macroscopic resonant tunneling operations.Furthermore, as previously described, realizing L_(Jp)>L_(Gp) may reduceW_(phi). The resulting improved spectral resolution of probe qubit 300can facilitate many aspects of quantum processor operation, including:the new mode of use described herein (i.e., determining eigenvalues of aHamiltonian), device calibration procedures, scientific experimentsinvolving magnetic resonant tunneling, etc.

In some implementations, it may be advantageous for the total inductanceof a probe qubit L_(Tp) to be substantially equal to the totalinductance of each computation qubit L_(Tc) in a quantum processorarchitecture. In such cases, the Josephson inductance L_(Jp) of theprobe qubit may be designed (i.e., by employing an appropriate number Nof additional Josephson junctions) to compensate for and/or offset thedecrease in the geometric inductance L_(Gp) that results from thereduced wiring length such that the total inductance L_(Tp) remainssubstantially unchanged.

Furthermore, probe qubits may not need to be strictly coherent. Acoherent qubit may have a long dephasing time. The longest reproducibledephasing times reported, vary from about 1 ns to about 10 μs. Dephasingof a qubit may occur from noise as well as coupling to the environment.Eliminating noise and removing coupling to the environment are centralchallenges in qubit engineering. Therefore, another advantage of using aprobe qubit is the relaxed need for the probe qubit to be coherent.

As illustrated in FIG. 3, Josephson junctions 330-339 are larger thanJosephson junctions 321 and 322 that make up compound Josephson junction302. In probe qubit 300, Josephson junctions 330-339 are large in orderto provide substantial Josephson inductance. A person of skill in theart will appreciate, in light of this disclosure, that the sizes of theJosephson junctions in a probe qubit may vary in differentimplementations.

Probe qubit 300 is programmed and/or controlled via a programmingsubsystem comprising programming interfaces 341 and 342. Programminginterface 341 couples flux signals to loop of superconducting material301 in order to control the energy bias (i.e., energy bias values, or“tilt”) of probe qubit 300 and programming interfaces 342 couples fluxsignals to compound Josephson junction 302 in order to control thetunneling energy (i.e., the barrier height) of probe qubit 300. Theprogramming subsystem used to program a probe qubit may comprisecomponents of a programming subsystem used to program computation qubitsand/or other elements of a quantum processor.

FIG. 4 is a schematic diagram of a quantum processor 400 that includes adedicated probe qubit 450 in accordance with the present systems andmethods. Processor 400 comprises two superconducting flux qubits 401,402 with a tunable ZZ-coupler 411 providing tunable communicativecoupling therebetween. Probe quit 450 comprises a loop ofsuperconducting material interrupted by a compound Josephson junctionand several (i.e., ten) serially-connected Josephson junctions. Inprocessor 400, qubits 401 and 402 are operated as computation qubits andprobe qubit 450 is directly communicatively coupleable to qubit 401 viadirect inductive coupling. In alternative implementations, probe qubit450 may be directly communicatively coupled to a computation qubit(e.g., to qubit 401) via direct galvanic coupling, or probe qubit 450may be indirectly communicatively coupleable to a computation qubit(e.g., to qubit 401) by a coupling device (such as coupler 411)—see, forexample, FIG. 5. FIG. 5 is a schematic diagram of another exampleimplementation of a quantum processor 500 that includes a dedicatedprobe qubit in accordance with the present systems and methods. The samereference numbers as used in FIG. 4 are used in FIG. 5 to denote thesame or similar elements. Quantum processor 500 includes a couplingdevice 501. Probe qubit 450 is indirectly communicatively coupled tocomputation qubit 401 via coupling device 501.

In accordance with the present systems and methods, probe qubit 450employs significantly less wiring than computation qubits 401 and 402.For example, computation qubits 401 and 402 each include a respectiveloop of superconducting material of length ˜X₁, whereas probe qubit 450includes a loop of superconducting material having length <X₁. As aresult, probe qubit 450 has a significantly lower geometric inductancethan computation qubits 401 and 402 (i.e., L_(Gp)<L_(Gc)) and issubjected to less noise from defects present in the qubit wiring and/ordielectric layers of processor 400. Probe qubit 450 also includes moreJosephson junctions than computation qubits 401 and 402 (e.g., ten moreJosephson junctions) which maintain the total inductance of probe qubit450 (L_(Tp)˜L_(Gp)+L_(Jp)) at a range suitable for macroscopic resonanttunneling operations by augmenting the Josephson inductance of probequbit 450 relative to that of computation qubits 401 and 402 (i.e.,L_(Jp)>L_(Jc)). In some implementations, it is advantageous to include anumber N of Josephson junctions in probe qubit 450 that provides aJosephson inductance L_(Jp) that at least approximately compensates forand/or offsets the reduction in the geometric inductance L_(Gp) of probequbit 450 resulting from the reduction in the length of wiring of probequbit 450 relative to computation qubits 401 ad 402, such that the totalinductance L_(Tp) of probe qubit 450 at least approximately equals therespective total inductance L_(Tc) of each of computation qubits 401 and402 (i.e., L_(Tp)˜L_(Tc)). Depending on the specific configuration beingimplemented, N may be equal to 1, or N may be greater than or equal to2. Furthermore, probe qubit 450 has a lower persistent current than thepersistent current of computation qubit 401. For example, the persistentcurrent of probe qubit 450 is approximately half of that of computationqubit 401. As previously described, the reduced I_(p) of probe qubit 450and/or increased L_(Jp) may help reduce R of Equation 4 resulting inimproved spectral resolution of probe qubit 450 communicatively coupledto computation qubit 401.

Processor 400 comprises two computation qubits 401, 402 and one probequbit 450, where the one probe qubit 450 is communicatively coupleableto one of the computation qubits (i.e., to qubit 401). Processor 400represents a scaled-down, simplified example of a processor that hasbeen adapted to facilitate the new modes of use described herein. Inpractice, a processor may implement any number of computation qubits andany number of probe qubits; a single probe qubit may be communicativelycoupleable to more than one computation qubit; and/or a singlecomputation qubit may be communicatively coupleable to more than oneprobe qubit. For example, in an alternative implementation, processor400 may include at least one additional probe qubit (i.e., at least asecond probe qubit, not shown) that is communicatively coupleable to atleast one of computation qubits 401 and/or 402, and/or processor 400 mayinclude many more computation qubits (i.e., on the order of tens,hundreds, thousands, or millions of computation qubits).

Throughout this specification and the appended claims, the term“programming subsystem” is used to generally describe the programmingelements (e.g., programming interfaces 121-125 of FIG. 1) included in aquantum processor (e.g., portion of quantum processor 100 of FIG. 1) andother associated control circuitry or instructions. As previouslydescribed, the programming subsystem may be separate from the quantumprocessor or included locally on the processor.

The above description of illustrated embodiments, including what isdescribed in the Abstract, is not intended to be exhaustive or to limitthe embodiments to the precise forms disclosed. Although specificembodiments of and examples are described herein for illustrativepurposes, various equivalent modifications can be made without departingfrom the spirit and scope of the disclosure, as will be recognized bythose skilled in the relevant art. The teachings provided herein of thevarious embodiments can be applied to other methods of quantumcomputation, not necessarily the exemplary methods for quantumcomputation generally described above.

The various embodiments described above can be combined to providefurther embodiments. All of the U.S. patents, U.S. patent applicationpublications, U.S. patent applications, International (PCT) patentapplications referred to in this specification and/or listed in theApplication Data Sheet including U.S. provisional patent applicationSer. No. 61/832,645 filed Jun. 7, 2013, are incorporated herein byreference, in their entirety. Aspects of the embodiments can bemodified, if necessary, to employ systems, circuits and concepts of thevarious patents, applications and publications to provide yet furtherembodiments.

These and other changes can be made to the embodiments in light of theabove-detailed description. In general, in the following claims, theterms used should not be construed to limit the claims to the specificembodiments disclosed in the specification and the claims, but should beconstrued to include all possible embodiments along with the full scopeof equivalents to which such claims are entitled. Accordingly, theclaims are not limited by the disclosure.

The invention claimed is:
 1. A quantum processor comprising asuperconducting qubit, the superconducting qubit comprising: a loop ofsuperconducting material having a geometric inductance L_(Gp); and acompound Josephson junction that interrupts the loop of superconductingmaterial, wherein the compound Josephson junction includes at least twoJosephson junctions that are superconductingly electrically coupled inparallel with one another with respect to the loop of superconductingmaterial, wherein the superconducting qubit has a Josephson inductanceL_(Jp) greater than the geometric inductance L_(Gp), the superconductingqubit further comprising: a number N of Josephson junctions thatinterrupt the loop of superconducting material, the N Josephsonjunctions being superconductingly electrically coupled in series withthe compound Josephson junction and superconductingly electricallycoupled in series with one another with respect to the loop ofsuperconducting material, and wherein the N Josephson junctionspositively contribute to the Josephson inductance L_(Jp).
 2. The quantumprocessor of claim 1 wherein N≥2.
 3. The quantum processor of claim 1further comprising: a plurality of superconducting flux qubits, whereinthe plurality of superconducting flux qubits define a Hamiltonian; aninductive coupling device to couple the loop of superconducting materialto at least one flux qubit from the plurality of superconducting fluxqubits with coupling strength J; and a local bias system for applying alocal bias with magnitude of about 2J and sign opposite to the couplingstrength, to the at least one flux qubit from the plurality ofsuperconducting flux qubits.
 4. The quantum processor of claim 3 whereinthe loop of superconducting material has a persistent current, the valueof the persistent current is less than the respective persistentcurrents of the at least one flux qubit from the plurality ofsuperconducting flux qubits.
 5. The quantum processor of claim 4 furthercomprising: a programming interface in a programming subsystem to applya magnetic field to the compound Josephson junction that interrupts theloop of superconducting material, wherein varying the magnetic fieldadjusts the persistent current in the loop of superconducting material.6. A quantum processor comprising: a plurality of computation qubits,wherein each computation qubit is a superconducting flux qubit thatcomprises, respectively: a loop of superconducting material having alength of at least X₁ and a geometric inductance of at least L_(Gc); anda compound Josephson junction that interrupts the loop ofsuperconducting material, wherein the computation qubit has a Josephsoninductance of at most L_(Jc), and the Josephson inductance L_(Jc) isless than the geometric inductance L_(Gc), at least one coupling devicethat provides tunable communicative coupling between a set of thecomputation qubits, wherein the at least one coupling device includes aloop of superconducting material interrupted by at least one Josephsonjunction; and one or more probe qubits wherein each probe qubit is asuperconducting flux qubit comprising, respectively: a loop ofsuperconducting material having a length less than X₁ and a geometricinductance L_(Gp); and a compound Josephson junction that interrupts theloop of superconducting material of the probe qubit, wherein thecompound Josephson junction includes at least two Josephson junctionsthat are superconductingly electrically coupled in parallel with oneanother with respect to the loop of superconducting material of theprobe qubit; wherein a Josephson inductance L_(Jp) of the probe qubit isgreater than the geometric inductance L_(Gp), and wherein at least oneof the probe qubits is communicatively coupleable to at least one of thecomputation qubits, and wherein at least one of the probe qubits furtherincludes a number N of Josephson junctions that interrupt the loop ofsuperconducting material of the probe qubit, the N Josephson junctionsbeing superconductingly electrically coupled in series with the compoundJosephson junction of the probe qubit and superconductingly electricallycoupled in series with one another with respect to the loop ofsuperconducting material of the probe qubit, and wherein the N Josephsonjunctions positively contribute to the Josephson inductance L_(Jp) ofthe probe qubit.
 7. The quantum processor of claim 6 wherein eachcomputation qubit has a total inductance L_(Tc) equal to a sum of thegeometric inductance L_(Gc) and the Josephson inductance L_(Jc), eachprobe qubit has a total inductance L_(Tp) equal to a sum of thegeometric inductance L_(Gp) and the Josephson inductance L_(Jp), and thetotal inductance of each probe qubit L_(Tp) is at least approximatelyequal to the total inductance of each computation qubit L_(Tc).
 8. Thequantum processor of claim 6 wherein each probe qubit is directlycommunicatively coupleable to at least one of the computation qubits viaat least one of galvanic coupling or inductive coupling.
 9. The quantumprocessor of claim 6, further comprising: a coupling device thatprovides tunable communicative coupling between at least one of theprobe qubits and at least one of the computation qubits, wherein thecoupling device includes a loop of superconducting material interruptedby at least one Josephson junction, and wherein the at least one probequbit is communicatively coupleable to at least one of the computationqubits via the coupling device.
 10. The quantum processor of claim 6wherein at least one of the probe qubits further comprises a firstpersistent current and each of the at least one computation qubitscommunicatively coupleable to the at least one of the probe qubitsfurther comprises a second persistent current and wherein the firstpersistent current is lower than the second persistent current.